/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) BR [EQUIVALENT, 0 ms] (2) HASKELL (3) COR [EQUIVALENT, 0 ms] (4) HASKELL (5) Narrow [SOUND, 0 ms] (6) QDP (7) MRRProof [EQUIVALENT, 39 ms] (8) QDP (9) NonTerminationLoopProof [COMPLETE, 0 ms] (10) NO (11) Narrow [COMPLETE, 0 ms] (12) TRUE ---------------------------------------- (0) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data MyInt = Pos Main.Nat | Neg Main.Nat ; data Main.Nat = Succ Main.Nat | Zero ; data Main.WHNF a = WHNF a ; dsEm :: (b -> a) -> b -> a; dsEm f x = Main.seq x (f x); enforceWHNF :: Main.WHNF b -> a -> a; enforceWHNF (Main.WHNF x) y = y; enumFromMyInt :: MyInt -> List MyInt; enumFromMyInt = numericEnumFrom; fromIntMyInt :: MyInt -> MyInt; fromIntMyInt x = x; numericEnumFrom n = Cons n (dsEm numericEnumFrom (psMyInt n (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))))); primMinusNat :: Main.Nat -> Main.Nat -> MyInt; primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero; primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y); primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x); primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y; primPlusInt :: MyInt -> MyInt -> MyInt; primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y; primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x; primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y); primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y); primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; primPlusNat Main.Zero Main.Zero = Main.Zero; primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); psMyInt :: MyInt -> MyInt -> MyInt; psMyInt = primPlusInt; seq :: a -> b -> b; seq x y = Main.enforceWHNF (Main.WHNF x) y; } ---------------------------------------- (1) BR (EQUIVALENT) Replaced joker patterns by fresh variables and removed binding patterns. ---------------------------------------- (2) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data MyInt = Pos Main.Nat | Neg Main.Nat ; data Main.Nat = Succ Main.Nat | Zero ; data Main.WHNF a = WHNF a ; dsEm :: (b -> a) -> b -> a; dsEm f x = Main.seq x (f x); enforceWHNF :: Main.WHNF a -> b -> b; enforceWHNF (Main.WHNF x) y = y; enumFromMyInt :: MyInt -> List MyInt; enumFromMyInt = numericEnumFrom; fromIntMyInt :: MyInt -> MyInt; fromIntMyInt x = x; numericEnumFrom n = Cons n (dsEm numericEnumFrom (psMyInt n (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))))); primMinusNat :: Main.Nat -> Main.Nat -> MyInt; primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero; primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y); primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x); primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y; primPlusInt :: MyInt -> MyInt -> MyInt; primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y; primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x; primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y); primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y); primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; primPlusNat Main.Zero Main.Zero = Main.Zero; primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); psMyInt :: MyInt -> MyInt -> MyInt; psMyInt = primPlusInt; seq :: b -> a -> a; seq x y = Main.enforceWHNF (Main.WHNF x) y; } ---------------------------------------- (3) COR (EQUIVALENT) Cond Reductions: The following Function with conditions "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (4) Obligation: mainModule Main module Main where { import qualified Prelude; data List a = Cons a (List a) | Nil ; data MyInt = Pos Main.Nat | Neg Main.Nat ; data Main.Nat = Succ Main.Nat | Zero ; data Main.WHNF a = WHNF a ; dsEm :: (b -> a) -> b -> a; dsEm f x = Main.seq x (f x); enforceWHNF :: Main.WHNF a -> b -> b; enforceWHNF (Main.WHNF x) y = y; enumFromMyInt :: MyInt -> List MyInt; enumFromMyInt = numericEnumFrom; fromIntMyInt :: MyInt -> MyInt; fromIntMyInt x = x; numericEnumFrom n = Cons n (dsEm numericEnumFrom (psMyInt n (fromIntMyInt (Main.Pos (Main.Succ Main.Zero))))); primMinusNat :: Main.Nat -> Main.Nat -> MyInt; primMinusNat Main.Zero Main.Zero = Main.Pos Main.Zero; primMinusNat Main.Zero (Main.Succ y) = Main.Neg (Main.Succ y); primMinusNat (Main.Succ x) Main.Zero = Main.Pos (Main.Succ x); primMinusNat (Main.Succ x) (Main.Succ y) = primMinusNat x y; primPlusInt :: MyInt -> MyInt -> MyInt; primPlusInt (Main.Pos x) (Main.Neg y) = primMinusNat x y; primPlusInt (Main.Neg x) (Main.Pos y) = primMinusNat y x; primPlusInt (Main.Neg x) (Main.Neg y) = Main.Neg (primPlusNat x y); primPlusInt (Main.Pos x) (Main.Pos y) = Main.Pos (primPlusNat x y); primPlusNat :: Main.Nat -> Main.Nat -> Main.Nat; primPlusNat Main.Zero Main.Zero = Main.Zero; primPlusNat Main.Zero (Main.Succ y) = Main.Succ y; primPlusNat (Main.Succ x) Main.Zero = Main.Succ x; primPlusNat (Main.Succ x) (Main.Succ y) = Main.Succ (Main.Succ (primPlusNat x y)); psMyInt :: MyInt -> MyInt -> MyInt; psMyInt = primPlusInt; seq :: a -> b -> b; seq x y = Main.enforceWHNF (Main.WHNF x) y; } ---------------------------------------- (5) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="enumFromMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="enumFromMyInt vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="numericEnumFrom vx3",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="Cons vx3 (dsEm numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3]; 6[label="dsEm numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 8[label="",style="dashed", color="red", weight=0]; 7[label="seq (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))) (numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];7 -> 9[label="",style="dashed", color="magenta", weight=3]; 9 -> 4[label="",style="dashed", color="red", weight=0]; 9[label="numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero))))",fontsize=16,color="magenta"];9 -> 10[label="",style="dashed", color="magenta", weight=3]; 8[label="seq (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))) vx4",fontsize=16,color="black",shape="triangle"];8 -> 11[label="",style="solid", color="black", weight=3]; 10[label="psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3]; 11 -> 13[label="",style="dashed", color="red", weight=0]; 11[label="enforceWHNF (WHNF (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero))))) vx4",fontsize=16,color="magenta"];11 -> 14[label="",style="dashed", color="magenta", weight=3]; 12[label="primPlusInt vx3 (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];40[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 40[label="",style="solid", color="burlywood", weight=9]; 40 -> 15[label="",style="solid", color="burlywood", weight=3]; 41[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 41[label="",style="solid", color="burlywood", weight=9]; 41 -> 16[label="",style="solid", color="burlywood", weight=3]; 14 -> 10[label="",style="dashed", color="red", weight=0]; 14[label="psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="magenta"];13[label="enforceWHNF (WHNF vx5) vx4",fontsize=16,color="black",shape="triangle"];13 -> 17[label="",style="solid", color="black", weight=3]; 15[label="primPlusInt (Pos vx30) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3]; 16[label="primPlusInt (Neg vx30) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3]; 17[label="vx4",fontsize=16,color="green",shape="box"];18[label="primPlusInt (Pos vx30) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="primPlusInt (Neg vx30) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="Pos (primPlusNat vx30 (Succ Zero))",fontsize=16,color="green",shape="box"];20 -> 22[label="",style="dashed", color="green", weight=3]; 21[label="primMinusNat (Succ Zero) vx30",fontsize=16,color="burlywood",shape="box"];42[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];21 -> 42[label="",style="solid", color="burlywood", weight=9]; 42 -> 23[label="",style="solid", color="burlywood", weight=3]; 43[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 43[label="",style="solid", color="burlywood", weight=9]; 43 -> 24[label="",style="solid", color="burlywood", weight=3]; 22[label="primPlusNat vx30 (Succ Zero)",fontsize=16,color="burlywood",shape="box"];44[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 44[label="",style="solid", color="burlywood", weight=9]; 44 -> 25[label="",style="solid", color="burlywood", weight=3]; 45[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 45[label="",style="solid", color="burlywood", weight=9]; 45 -> 26[label="",style="solid", color="burlywood", weight=3]; 23[label="primMinusNat (Succ Zero) (Succ vx300)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 24[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 25[label="primPlusNat (Succ vx300) (Succ Zero)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 26[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 27[label="primMinusNat Zero vx300",fontsize=16,color="burlywood",shape="box"];46[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];27 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 31[label="",style="solid", color="burlywood", weight=3]; 47[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 32[label="",style="solid", color="burlywood", weight=3]; 28[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];29[label="Succ (Succ (primPlusNat vx300 Zero))",fontsize=16,color="green",shape="box"];29 -> 33[label="",style="dashed", color="green", weight=3]; 30[label="Succ Zero",fontsize=16,color="green",shape="box"];31[label="primMinusNat Zero (Succ vx3000)",fontsize=16,color="black",shape="box"];31 -> 34[label="",style="solid", color="black", weight=3]; 32[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];32 -> 35[label="",style="solid", color="black", weight=3]; 33[label="primPlusNat vx300 Zero",fontsize=16,color="burlywood",shape="box"];48[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];33 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 36[label="",style="solid", color="burlywood", weight=3]; 49[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 37[label="",style="solid", color="burlywood", weight=3]; 34[label="Neg (Succ vx3000)",fontsize=16,color="green",shape="box"];35[label="Pos Zero",fontsize=16,color="green",shape="box"];36[label="primPlusNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3]; 37[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3]; 38[label="Succ vx3000",fontsize=16,color="green",shape="box"];39[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: new_numericEnumFrom(vx3) -> new_numericEnumFrom(new_psMyInt(vx3)) The TRS R consists of the following rules: new_psMyInt(Main.Neg(Main.Zero)) -> Main.Pos(Main.Succ(Main.Zero)) new_psMyInt(Main.Neg(Main.Succ(Main.Zero))) -> Main.Pos(Main.Zero) new_primPlusNat(Main.Zero) -> Main.Succ(Main.Zero) new_primPlusNat(Main.Succ(vx300)) -> Main.Succ(Main.Succ(new_primPlusNat0(vx300))) new_psMyInt(Main.Pos(vx30)) -> Main.Pos(new_primPlusNat(vx30)) new_psMyInt(Main.Neg(Main.Succ(Main.Succ(vx3000)))) -> Main.Neg(Main.Succ(vx3000)) new_primPlusNat0(Main.Succ(vx3000)) -> Main.Succ(vx3000) new_primPlusNat0(Main.Zero) -> Main.Zero The set Q consists of the following terms: new_psMyInt(Main.Neg(Main.Succ(Main.Zero))) new_primPlusNat0(Main.Zero) new_psMyInt(Main.Pos(x0)) new_psMyInt(Main.Neg(Main.Succ(Main.Succ(x0)))) new_psMyInt(Main.Neg(Main.Zero)) new_primPlusNat(Main.Zero) new_primPlusNat0(Main.Succ(x0)) new_primPlusNat(Main.Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (7) MRRProof (EQUIVALENT) By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. Strictly oriented rules of the TRS R: new_psMyInt(Main.Neg(Main.Zero)) -> Main.Pos(Main.Succ(Main.Zero)) new_psMyInt(Main.Neg(Main.Succ(Main.Zero))) -> Main.Pos(Main.Zero) Used ordering: Polynomial interpretation [POLO]: POL(Main.Neg(x_1)) = 2 + 2*x_1 POL(Main.Pos(x_1)) = 2 + x_1 POL(Main.Succ(x_1)) = x_1 POL(Main.Zero) = 2 POL(new_numericEnumFrom(x_1)) = x_1 POL(new_primPlusNat(x_1)) = x_1 POL(new_primPlusNat0(x_1)) = x_1 POL(new_psMyInt(x_1)) = x_1 ---------------------------------------- (8) Obligation: Q DP problem: The TRS P consists of the following rules: new_numericEnumFrom(vx3) -> new_numericEnumFrom(new_psMyInt(vx3)) The TRS R consists of the following rules: new_primPlusNat(Main.Zero) -> Main.Succ(Main.Zero) new_primPlusNat(Main.Succ(vx300)) -> Main.Succ(Main.Succ(new_primPlusNat0(vx300))) new_psMyInt(Main.Pos(vx30)) -> Main.Pos(new_primPlusNat(vx30)) new_psMyInt(Main.Neg(Main.Succ(Main.Succ(vx3000)))) -> Main.Neg(Main.Succ(vx3000)) new_primPlusNat0(Main.Succ(vx3000)) -> Main.Succ(vx3000) new_primPlusNat0(Main.Zero) -> Main.Zero The set Q consists of the following terms: new_psMyInt(Main.Neg(Main.Succ(Main.Zero))) new_primPlusNat0(Main.Zero) new_psMyInt(Main.Pos(x0)) new_psMyInt(Main.Neg(Main.Succ(Main.Succ(x0)))) new_psMyInt(Main.Neg(Main.Zero)) new_primPlusNat(Main.Zero) new_primPlusNat0(Main.Succ(x0)) new_primPlusNat(Main.Succ(x0)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (9) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_numericEnumFrom(vx3) evaluates to t =new_numericEnumFrom(new_psMyInt(vx3)) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [vx3 / new_psMyInt(vx3)] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_numericEnumFrom(vx3) to new_numericEnumFrom(new_psMyInt(vx3)). ---------------------------------------- (10) NO ---------------------------------------- (11) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="enumFromMyInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="enumFromMyInt vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="numericEnumFrom vx3",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="Cons vx3 (dsEm numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))))",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3]; 6[label="dsEm numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero))))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 8[label="",style="dashed", color="red", weight=0]; 7[label="seq (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))) (numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))))",fontsize=16,color="magenta"];7 -> 9[label="",style="dashed", color="magenta", weight=3]; 9 -> 4[label="",style="dashed", color="red", weight=0]; 9[label="numericEnumFrom (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero))))",fontsize=16,color="magenta"];9 -> 10[label="",style="dashed", color="magenta", weight=3]; 8[label="seq (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))) vx4",fontsize=16,color="black",shape="triangle"];8 -> 11[label="",style="solid", color="black", weight=3]; 10[label="psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="triangle"];10 -> 12[label="",style="solid", color="black", weight=3]; 11 -> 13[label="",style="dashed", color="red", weight=0]; 11[label="enforceWHNF (WHNF (psMyInt vx3 (fromIntMyInt (Pos (Succ Zero))))) vx4",fontsize=16,color="magenta"];11 -> 14[label="",style="dashed", color="magenta", weight=3]; 12[label="primPlusInt vx3 (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];40[label="vx3/Pos vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 40[label="",style="solid", color="burlywood", weight=9]; 40 -> 15[label="",style="solid", color="burlywood", weight=3]; 41[label="vx3/Neg vx30",fontsize=10,color="white",style="solid",shape="box"];12 -> 41[label="",style="solid", color="burlywood", weight=9]; 41 -> 16[label="",style="solid", color="burlywood", weight=3]; 14 -> 10[label="",style="dashed", color="red", weight=0]; 14[label="psMyInt vx3 (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="magenta"];13[label="enforceWHNF (WHNF vx5) vx4",fontsize=16,color="black",shape="triangle"];13 -> 17[label="",style="solid", color="black", weight=3]; 15[label="primPlusInt (Pos vx30) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3]; 16[label="primPlusInt (Neg vx30) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3]; 17[label="vx4",fontsize=16,color="green",shape="box"];18[label="primPlusInt (Pos vx30) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3]; 19[label="primPlusInt (Neg vx30) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3]; 20[label="Pos (primPlusNat vx30 (Succ Zero))",fontsize=16,color="green",shape="box"];20 -> 22[label="",style="dashed", color="green", weight=3]; 21[label="primMinusNat (Succ Zero) vx30",fontsize=16,color="burlywood",shape="box"];42[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];21 -> 42[label="",style="solid", color="burlywood", weight=9]; 42 -> 23[label="",style="solid", color="burlywood", weight=3]; 43[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];21 -> 43[label="",style="solid", color="burlywood", weight=9]; 43 -> 24[label="",style="solid", color="burlywood", weight=3]; 22[label="primPlusNat vx30 (Succ Zero)",fontsize=16,color="burlywood",shape="box"];44[label="vx30/Succ vx300",fontsize=10,color="white",style="solid",shape="box"];22 -> 44[label="",style="solid", color="burlywood", weight=9]; 44 -> 25[label="",style="solid", color="burlywood", weight=3]; 45[label="vx30/Zero",fontsize=10,color="white",style="solid",shape="box"];22 -> 45[label="",style="solid", color="burlywood", weight=9]; 45 -> 26[label="",style="solid", color="burlywood", weight=3]; 23[label="primMinusNat (Succ Zero) (Succ vx300)",fontsize=16,color="black",shape="box"];23 -> 27[label="",style="solid", color="black", weight=3]; 24[label="primMinusNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];24 -> 28[label="",style="solid", color="black", weight=3]; 25[label="primPlusNat (Succ vx300) (Succ Zero)",fontsize=16,color="black",shape="box"];25 -> 29[label="",style="solid", color="black", weight=3]; 26[label="primPlusNat Zero (Succ Zero)",fontsize=16,color="black",shape="box"];26 -> 30[label="",style="solid", color="black", weight=3]; 27[label="primMinusNat Zero vx300",fontsize=16,color="burlywood",shape="box"];46[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];27 -> 46[label="",style="solid", color="burlywood", weight=9]; 46 -> 31[label="",style="solid", color="burlywood", weight=3]; 47[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];27 -> 47[label="",style="solid", color="burlywood", weight=9]; 47 -> 32[label="",style="solid", color="burlywood", weight=3]; 28[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];29[label="Succ (Succ (primPlusNat vx300 Zero))",fontsize=16,color="green",shape="box"];29 -> 33[label="",style="dashed", color="green", weight=3]; 30[label="Succ Zero",fontsize=16,color="green",shape="box"];31[label="primMinusNat Zero (Succ vx3000)",fontsize=16,color="black",shape="box"];31 -> 34[label="",style="solid", color="black", weight=3]; 32[label="primMinusNat Zero Zero",fontsize=16,color="black",shape="box"];32 -> 35[label="",style="solid", color="black", weight=3]; 33[label="primPlusNat vx300 Zero",fontsize=16,color="burlywood",shape="box"];48[label="vx300/Succ vx3000",fontsize=10,color="white",style="solid",shape="box"];33 -> 48[label="",style="solid", color="burlywood", weight=9]; 48 -> 36[label="",style="solid", color="burlywood", weight=3]; 49[label="vx300/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 49[label="",style="solid", color="burlywood", weight=9]; 49 -> 37[label="",style="solid", color="burlywood", weight=3]; 34[label="Neg (Succ vx3000)",fontsize=16,color="green",shape="box"];35[label="Pos Zero",fontsize=16,color="green",shape="box"];36[label="primPlusNat (Succ vx3000) Zero",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3]; 37[label="primPlusNat Zero Zero",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3]; 38[label="Succ vx3000",fontsize=16,color="green",shape="box"];39[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) TRUE